Semi-cubic Hyponormality of Weighted Shifts with Stampfli Recursive Tail

Baek, Seung‐Hwan; Exner, George R.; Jung, Il Bong; Li, Chunji

doi:10.1007/s00020-017-2373-y

Cited by 3 publications

(2 citation statements)

References 23 publications

(84 reference statements)

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“…Here, since η(t) has exactly one critical number 4 3 20 on R + and η ′′ (t) > 0 on R + , η(t) has a positive minimum at 4 3 20 . So, ρ 14 100 , t is negative and since C is a loop in the first quadrant, C lies on the left side of a line h = 14 100 .…”

Section: The Shape Of the Region With Semi-cubic Hyponormalitymentioning

confidence: 99%

On Semi-cubically Hyponormal Weighted Shifts with First Two Equal Weights

Baek¹,

Jung²,

Exner³

et al. 2016

Kyungpook mathematical journal

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Abstract. It is known that a semi-cubically hyponormal weighted shift need not satisfy the flatness property, in which equality of two weights forces all or almost all weights to be equal. So it is a natural question to describe all semi-cubically hyponormal weighted shifts Wα with first two weights equal. Let α : 1, 1,∧ be a backward 3-step extension of a recursively generated weight sequence with 1 < x < u < v < w and let Wα be the associated weighted shift. In this paper we characterize completely the semicubical hyponormal Wα satisfying the additional assumption of the positive determinant coefficient property, which result is parallel to results for quadratic hyponormality.

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Section: The Shape Of the Region With Semi-cubic Hyponormalitymentioning

confidence: 99%

On Semi-cubically Hyponormal Weighted Shifts with First Two Equal Weights

Baek¹,

Jung²,

Exner³

et al. 2016

Kyungpook mathematical journal

Self Cite

View full text Add to dashboard Cite

show abstract

“…An operator T in L(H) is said to be weakly n-hyponormal if p(T) is hyponormal for any polynomial p with degree less than or equal to n. An operator T is polynomially hyponormal if p(T) is hyponormal for every polynomial p. In particular, the weak two-hyponormality (or weak three-hyponormality) is referred to as quadratical hyponormality (or cubical hyponormality, resp.) and has been considered in detail in [1][2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%